Pour brown sugar into the bowl of an electric stand mixer. Pour in vegetable oil and applesauce, set mixer with paddle attachment and blend until well combined. Mix in eggs and vanilla. Add in 1/3 of the flour mixture and mix on low speed until combined, then blend in 1/2 of the buttermilk. Add another 1/3 of the flour mixture and other half of buttermilk. Finish by adding remaining 1/3 of flour and mix until well combined. Divide mixture evenly among prepared baking pans. Bake in preheated oven until toothpick inserted into center comes out clean, about 28 - 32 minutes. Allow to cool several minutes then run a knife around edges to ensure cake is loose and invert upside down onto a wire rack to cool. Cool completely then level tops of cakes as needed.